Three-Dimensional Finite Element Modelling of Thermomechanics and Macrosegregation in Binary Alloys Solidification

FACHINOTTI, V. D.; BELLET, M.

Salerno

Conferencia; 6th International ESAFORM Conference on Material Forming; 2003

European Scientific Association For Material Forming (ESAFORM)

This work introduces a numerical model for the coupled solution of momentum, energy and solute conservation equations in the three-dimensional space, especially addressed to binary alloys solidification. The spatial discretisation is carried out using linear tetrahedral finite elements, particularly those of P1/P1+-type for the momentum equation. Momentum equations resemble the Navier-Stokes equations for the completely liquid material. Binary alloys solidification is characterised by the formation of a solid-liquid (or mushy) region. The interdendritic flow in this region is assumed to be governed by the Darcy’s law for a porous medium, whose permeability is defined by the Carman-Kozeny formula. In such a way, the solid is modelled as a zero-permeable porous body. Thermal and solutal buoyancy forces are taken into account by means of the Boussinesq’s model. Microsegregation is governed by the lever rule, assuming the local equilibrium of composition at phase interfaces. The resulting solute advection-diffusion equation  is solved using the well-known Streamline-Upwind Petrov/Galerkin (SUPG) method. Momentum, energy and solute equations are coupled by a simple staggered scheme at each time step. The full algorithm was implemented in THERCAST, a three-dimensional finite-element code. Finally, we show an application of the model to the solidification of an iron-carbon alloy in a square cavity, comparing the results of  THERCAST to those of SOLID, a finite-volume code addressed to the solution of this problem in two-dimensional domains.